🧮 algebra

1. **State the problem:** We are given three points: (1, -6), (5, -7), and (9, -8). We need to determine which type of function or sequence these points represent and find an expli

1. **State the problem:** We are given two points on a graph, (2,2) and (6,1), and we want to find the exponential function of the form $$y = ab^x$$ that passes through these point

1. **State the problem:** We are given points (2, 2) and (6, -1) on a graph and asked to identify whether the graph represents an arithmetic sequence, geometric sequence, linear fu

1. **State the problem:** We are given two points on a graph: (2, 2) and (6, -1). We need to find the explicit formula of the linear function that passes through these points. 2. *

1. **Problem Statement:** We are given two points from a graph: (2, 2) and (6, -1). We need to determine which type of sequence or function the graph represents and find an explici

1. **State the problem:** We are given two points from a sequence plotted on a graph: $(1, -3)$ and $(2, -\frac{3}{2})$. We want to find the formula for the geometric sequence $a_n

1. **Problem statement:** Find the values of $x \in \mathbb{R}$ for which the series $$\sum_{k=2}^\infty \left(\frac{x+3}{2}\right)^k$$ converges, and find the sum of the series fo

1. **Problem Statement:** Given points (-3, -5), (1, -6), and (5, -7) on a graph, determine the type of function they represent and find an explicit formula for the function. 2. **

1. **Problem Statement:** Given points $(-3, -5)$, $(-1, -6)$, and $(5, -7)$, determine the type of sequence or function they represent and find an explicit formula matching the gr

1. **Stating the problem:** We are given a graph with points (0, -4), (1, -6), and (2, 9) and asked to identify the type of sequence or function it represents and find an explicit

1. **State the problem:** We want to find the values of $x \in \mathbb{R}$ for which the series $$\sum_{k=2}^\infty \left(\frac{x+3}{2}\right)^k$$ converges, and then find the sum

1. **Stating the problem:** We are given points (0, -4), (1, -6), and (2, -9) and asked to identify the type of sequence or function they represent. 2. **Check if it is an arithmet

1. **State the problem:** Find the equation of the function $f(x)$ that passes through the points $(-6, -6)$, $(-2, -7)$, and $(2, -8)$. 2. **Identify the type of function:** Since

1. **State the problem:** We are given three points on a graph: $(6,6)$, $(-2,7)$, and $(2,-8)$. We need to determine which type of function the graph represents and find an explic

1. The problem is to solve the inequality $-9 > 2x$ and find the values of $x$ that satisfy it. 2. To solve inequalities, we use similar rules as equations, but when multiplying or

1. The problem is to convert the fraction $\frac{1}{2}$ into a decimal number. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator.

1. **State the problem:** Multiply $\frac{1}{2}$ by 58.5. 2. **Formula used:** Multiplication of a fraction by a number is given by:

1. **State the problem:** Simplify the expression $\frac{1}{2} x - 58.5$. 2. **Understand the expression:** This is a linear expression in terms of $x$, where $\frac{1}{2} x$ means

1. **State the problem:** Simplify the expression $\frac{1}{4} - \frac{1}{2}$.\n\n2. **Recall the rule for subtracting fractions:** To subtract fractions, they must have the same d

1. **State the problem:** Calculate the sum of the fractions $-\frac{1}{5}$ and $\frac{3}{5}$. 2. **Formula and rules:** When adding fractions with the same denominator, add the nu

1. **State the problem:** We need to add the fractions $\frac{3}{10}$ and $-\frac{1}{5}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The sum i